<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>2215-3470</journal-id>
<journal-title><![CDATA[Uniciencia]]></journal-title>
<abbrev-journal-title><![CDATA[Uniciencia]]></abbrev-journal-title>
<issn>2215-3470</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional, Costa Rica]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2215-34702022000100253</article-id>
<article-id pub-id-type="doi">10.15359/ru.36-1.15</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Reconstrucción espectral de haces de fotones de kilovoltaje por medio de recocido simulado generalizado]]></article-title>
<article-title xml:lang="en"><![CDATA[Spectral reconstruction of kilovoltage photon beams using generalized simulated annealing]]></article-title>
<article-title xml:lang="pt"><![CDATA[Reconstrução espectral de feixes de fótons de kilovoltagem através do recozimento simulado generalizado]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Wilches-Visbal]]></surname>
<given-names><![CDATA[Jorge Homero]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Apaza-Veliz]]></surname>
<given-names><![CDATA[Danny Giancarlo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Nicolucci]]></surname>
<given-names><![CDATA[Patrícia]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad del Magdalena Facultad de Ciencias de la Salud ]]></institution>
<addr-line><![CDATA[Santa Marta ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidade de São Paulo Departamento de Física ]]></institution>
<addr-line><![CDATA[Ribeirão Preto ]]></addr-line>
<country>Brazil</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidade de São Paulo  Departamento de Física]]></institution>
<addr-line><![CDATA[Ribeirão Preto ]]></addr-line>
<country>Brazil</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<volume>36</volume>
<numero>1</numero>
<fpage>253</fpage>
<lpage>263</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S2215-34702022000100253&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S2215-34702022000100253&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S2215-34702022000100253&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Determinar el espectro de energía de dos haces de rayos X de kilovoltaje (kV), a partir de sus curvas de transmisión, mediante una metodología matemática basada en la transformada de Laplace y el algoritmo de transmisión se asociaron, por medio de una expresión matemática derivada de la solución analítica de la transformada de Laplace. Los datos de transmisión se calcularon relacionando el kerma de aire de los haces atenuados, al pasar por placas de aluminio de diferente espesor, con el de los no atenuados. La función de recocido simulado generalizada, desarrollada en un trabajo anterior, se empleó para descifrar los parámetros de la expresión y así obtener los espectros. La validación se realizó comparando las capas semirreductoras de las curvas de transmisión y las extraídas de los espectros. El error porcentual cuadrático medio entre los datos de transmisión y la curva de ajuste para cada espectro, definido a partir de los parámetros encontrados, fue inferior al 1 %, lo que indica un buen ajuste. Se observó el mismo error cuando se cotejó la primera capa semirreductora de las curvas de transmisión y las de cada espectro reconstruido. El tiempo de cálculo de los parámetros fue de 5 s para 80 kV y 14 s para 120 kV. En ningún caso se obtuvo una solución no realista de los espectros. Estos resultados fueron mejores que los de un trabajo anterior en el que se utilizaron mínimos cuadrados. La metodología de reconstrucción basada en recocido simulado generalizado, empleada en este manuscrito, pudo derivar de manera eficiente los espectros de dos haces de kilovoltaje con una precisión comparable a la de trabajos anteriores. Una limitación es que la validación no se realizó comparando con los espectros del equipo.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract  (Objective):  To unfold the energy spectrum of two kilovoltage (kV) X-ray beams from transmission curves through a mathematical methodology based on Laplace transform and the generalized simulated annealing algorithm.  (Methodology)  Energy spectra of photon beams and transmission data were associated by means of a mathematical expression derived from the analytical solution of Laplace transform. Transmission data was calculated by relating the air kerma of the attenuated beams, passing through aluminium plates of different thickness, to that of the non-attenuated beam. Generalized simulated annealing function, developed in an early work, was employed to find the parameters of the expression and so determine the spectra. Validation of the methodology was done by the comparison of the half-value layers obtained from transmission curves and the spectra.  (Results)  The mean square percentage error between transmission data and fitting curve of each spectrum defined from the parameters found was lower than 1% indicating a good adjustment. The same error was observed when the first half-value layer (HVL) from the transmission curves and those of each reconstructed spectrum were compared. Calculation time of parameters was 5 sec for 80 kV and 14 sec for 120 kV. In no case, non-realistic solution of energy spectra was obtained. These results were better than an early work where leastsquares were used.  (Conclusion)  The reconstruction methodology based on generalized simulated annealing employed in this manuscript can efficiently derive the spectra of two X-ray beams with comparable accuracy to previous work. A limitation is that validation was not done by comparing data with the equipment&#8217;s spectra.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo Encontrar o espectro de energia de dois feixes de raios-X de quilovoltagem a partir das curvas de transmissão por meio de uma metodologia matemática baseada na transformada de Laplace e no algoritmo de recozimento simulado generalizado. Os espectros de energia e os dados de transmissão foram associados por meio de uma expressão matemática derivada da solução analítica da transformada de Laplace. Os dados de transmissão foram calculados relacionando o kerma no ar dos feixes atenuados, ao passar por placas de alumínio de diferentes espessuras, com o dos feixes não atenuados. A função de recozimento simulado generalizado, desenvolvida em um trabalho anterior, foi empregada para encontrar os parâmetros da expressão para assim determinar os espectros. A validação da metodologia foi feita pela comparação das camadas semirredutoras obtidas das curvas de transmissão e dos espectros. O erro percentual médio quadrático entre os dados de transmissão e a curva de ajuste, para cada espectro definido a partir dos parâmetros encontrados, foi menor do que 1%, indicando um bom ajuste. O mesmo erro foi observado quando comparada a primeira camada semirredutora das curvas de transmissão e aquelas de cada espectro reconstruído. O tempo de cálculo dos parâmetros foi de 5 s para 80 kV e 14 s para 120 kV. Em nenhum caso, solução não realista dos espectros foi obtida. Os resultados foram melhores do que um trabalho anterior onde mínimos quadrados foram usados. A metodologia de reconstrução fundamentada no recozimento simulado generalizado, empregada neste trabalho, pôde derivar eficientemente os espectros de dois feixes de raios-X com precisão comparável a trabalhos anteriores. Uma limitação é que a validação não foi feita por comparação com os espectros do equipamento.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[photon spectra]]></kwd>
<kwd lng="en"><![CDATA[generalized simulated annealing]]></kwd>
<kwd lng="en"><![CDATA[inverse reconstruction]]></kwd>
<kwd lng="en"><![CDATA[transmission curves]]></kwd>
<kwd lng="es"><![CDATA[Espectros de fotones]]></kwd>
<kwd lng="es"><![CDATA[recocido simulado generalizado]]></kwd>
<kwd lng="es"><![CDATA[reconstrucción inversa]]></kwd>
<kwd lng="es"><![CDATA[curvas de transmisión]]></kwd>
<kwd lng="pt"><![CDATA[espectros de fótons]]></kwd>
<kwd lng="pt"><![CDATA[recozimento simulado generalizado]]></kwd>
<kwd lng="pt"><![CDATA[reconstrução inversa]]></kwd>
<kwd lng="pt"><![CDATA[curvas de transmissão.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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